On the proximity of multiplicative functions to the function counting prime factors with multiplicity

Theophilus Agama

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arXiv · 1706.08646

On the proximity of multiplicative functions to the function counting prime factors with multiplicity

Theophilus Agama

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Abstract

We examine how closely a multiplicative function resembles an additive function. Given a multiplicative function $g$ and an additive function $f$, we examine the size of the quantity $E(f,g;x)=\# \{n\leq x:f(n)=g(n)\}$. We establish a lower bound for $E(\Omega,g,x)$.

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Theophilus Agama. 2017-06-27. On the proximity of multiplicative functions to the function counting prime factors with multiplicity. https://arxiv.org/abs/1706.08646

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